Process and Energy Laboratory, Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands.
J Chem Phys. 2013 Jul 21;139(3):034505. doi: 10.1063/1.4815916.
An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under- and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition.
昂萨格第二维里理论的扩展被用来描述切线硬球链流体的各向同性-向列相转变。采用棒-环模型引入了柔性。通过对取向相关的对排除体积的精确解析逼近，描述了链柔性对第二维里系数的影响。这种逼近的使用允许通过使用单个纯组分参数来对分子内柔性进行解析处理。考虑了两种逼近更高维里系数影响的方法，即 Vega-Lago 重标度和 Scaled Particle Theory (SPT)。采用昂萨格试探函数来描述取向分布函数。状态方程和取向序参量的理论预测与蒙特卡罗 (MC) 模拟的结果进行了比较。对于长度为 9 及以上的线性链，理论结果与 MC 数据非常吻合。对于较短的链长，更高维里系数的逼近所引入的小误差变得明显，导致在相变处压力和密度差的低估和高估。对于合理刚性的棒-环流体，可以获得理论和 MC 模拟之间的定量比较。然而，对于更灵活的链，Vega-Lago 重标度和 SPT 都会导致相变位置的低估。
